In cellular radio systems that utilise a code division multiple access (CDMA) scheme, the transmissions from multiple users are sent simultaneously over the communication media and these different signals are distinguished from one another by the spreading codes. Typically orthogonal spreading codes are assigned to the different users of the system which makes it simple to separate the users at the receiver side. However, orthogonality between spreading codes may be lost if the transmissions occur over a frequency-selective channel such as a wireless radio channel having multiple propagation paths. In conditions such as these where the orthogonality between the codes and therefore the users is lost, the task of optimally separating the users at the receiving side is significantly more complicated.
In general, the complexity of performing optimal multiuser detection under such conditions grows exponentially with the number of active users. Approximate solutions to this detection problem therefore have to be targeted by real-life implementations. One important class of such approximate detectors is that of the linear detectors, which in basic terms approximate the true discrete-valued symbol prior distribution with a Gaussian prior distribution. This eliminates the combinatorial nature of the optimal detection problem.
For CDMA systems there are two distinct sub-classes of such linear detection. The first sub-class is that of linear chip-level equalisation, which in essence considers the transmitted chips as being independent in order to make implementation easier. The second sub-class is that of linear symbol-level equalisation which accounts for the coupling between the transmitted chips due to the spreading codes, resulting in optimal linear processing. As a result, linear symbol-level equalisation can achieve much better performance compared to that of linear chip-level equalisation, but this typically comes at the cost of significant additional computational complexity. This is especially true in CDMA systems such as 3rd Generation Partnership Project (3GPP) wideband CDMA (WCDMA) and high speed downlink packet access (HSDPA) systems, where the scrambling code has a very long period compared to the length of the spreading codes which requires that the symbol-level equalisation coefficients be recomputed for each use.
In practice the chip-level equalisation has generally been the norm in many CDMA systems, since the complexity of symbol-level equalisation has typically been out of reach for practical implementations.
It is well-known that optimal detection in CDMA systems generally requires joint detection over all active users and codes. If all active spreading codes and associated constellation types are known to the receiver, optimal detection is possible by basically searching for the combination that maximises the likelihood of the transmitted sequence of data symbols. Such an exhaustive search over the discrete space of all possible data symbol combinations is exponentially complex in the number of users and codes and is therefore out of reach for practical CDMA implementations. Instead, various sub-optimal approximate joint detection schemes have been conceived and these are typically classified by whether non-linear and linear operations are performed. Examples of approximate detectors based on linear processing are rake, chip- and symbol-level LMMSE (linear minimum mean squared error) equalisers, whereas examples of non-linear approximations include sphere detection and serial/parallel interference cancellation schemes.
An example of an efficient chip-level LMMSE equalisation implementation exploiting fast Fourier transforms (FFTs) is described in a paper by Y. Guo, D. McCain and J. R. Cavallaro, entitled “FFT-Accelerated Iterative MIMO Chip Equalizer Architecture For CDMA Downlink” [IEEE ICASSP, March 2005]. Approximations for a symbol-level LMMSE equalisation may be seen in a paper by M. Vollmer, M. Haardt and J. Gotze, entitled “Comparative study of joint-detection techniques for TD-CDMA based mobile radio systems” [IEEE Journal on Selected Areas in Communications, August 2001]. Also, solving the linear system of equations that arise for linear joint detection in a CDMA system using non-orthogonal spreading codes over a frequency-flat channel can be seen in a paper by C. B. Tjitrosoewarno, A. Fukasawa, and Y. Takizawa, entitled “Multi-user receiver using conjugate gradient method for wideband CDMA” [IEEE ISCAS, May 2005]. Finally, using the conjugate gradient algorithm for solving the linear system of equations that arise in an asynchronous CDMA system operating in a multipath channel is considered in a paper by A. Al Housseini, Th. Chonavel, T. Saoudi and M. Ammar entitled “Multi-user Detection in DS—CDMA Systems: a Conjugate-gradient implementation” [IEEE VTC Spring 2003].